# ST958: Topics in Mathematical Finance

**Lecturers: **

Professor David Hobson, Dr Martin Herdegen, Dr Gechun Liang

**Prerequisites**:

- Measure-theoretic Probability
- Students must have done either ST908 Probability
**or**ST401 Stochastic Methods in Finance.

**Restrictions:**

- Students who are not enrolled in the MSc in Financial Mathematics may take
*at most*two of the following modules:

• ST906 Financial Time Series.

• ST909 Continuous Time Finance for Interest Rate Models.

• ST958 Topics in Mathematical Finance.

**Commitment:**

- 3 hours of lectures per week. This module runs in Term 2.

**Aims:**

- To provide an introduction to three advanced topics in Mathematical Finance.
- Compute and explain key variables in the relevant models.
- Apply appropriate mathematical techniques.
- Analyse and compare different modelling approaches.

**This year's topics:**

- Introduction to risk measures
- Contagion risk and systemic risk
- Beyond the Black-Scholes model

Topics are motivated by current questions relevant to the financial industry. Topics may change each year. Each topic is taught by a different lecturer.

**Assessment:**

*Three*in-class tests: each worth 5% of final module mark.- Final 2h exam: worth 85% of final module mark.

**Illustrative Bibliography (for this year):**

- Föllmer, H. and Schied, A. (2016):
*Stochastic Finance*, 4th ed., de Gruyer. - McNeil, A., Frey, R. and Embrechts, P. (2015):
*Quantitative Risk Management, 2nd rev. ed.*, Princeton University Press. - Eisenberg, L., and Noe, T.H. (2001):
*Systemic risk in financial systems*, Management Science**47**(2), 236-249. - Collin‐Dufresne, P., Goldstein, R., and Hugonnier, J. (2004):
*A general formula for valuing defaultable securities*, Econometrica**72**(5), 1377-1407. - Gatheral, J. (2006):
*The volatility surface: a practitioner’s guide*, Wiley.